1. Field of the Invention
This invention relates to matrix multiplier systems and, more particularly, to such systems utilizing fiber optic coupling arrays.
2. Description of the Prior Art
The present invention performs a specific class of matrix operations. This operation is the multiplication of an N-dimensional vector by an N-by-M-dimensional matrix. The product of such an operation is an M-dimensional vector. In matrix algebra notation, the operation is written symbolically as EQU A=B.times.E, (1)
where B=B (b.sub.1, b.sub.2, . . . , b.sub.N) is an N-dimensional vector having N components b.sub.1, b.sub.2, . . . , b.sub.N ; ##EQU1## is an N-by-M-dimensional matrix having N-times-M components; and A=A (a.sub.1, a.sub.2, . . . , a.sub.M) is an M-dimensional vector. An alternative symbolic representation of matrix multiplication is written as follows: ##EQU2## where i and j are indices for the vector and matrix components (i=1, 2, . . . , M and j=1, 2, . . . , N), and the symbol ##EQU3## means that all of the products b.sub.j .times.e.sub.ji are summed for every value of j between 1 and N. Equation (2) is the formula by which the product components are calculated if the components b.sub.j and e.sub.ji are known.
Multiplication operations of the type indicated by Equations (1) and (2) conventionally are berformed by electronic digital binary computers. This conventional process is performed by loading each of the components to be multiplied (the b.sub.j s and the e.sub.ji s) into digital memory devices, extracting the components one-by-one from memory into an arithmetic logic unit (ALU), and then the ALU multiplies the components and stores the products in selected memory elements.
This operation of matrix multiplication is considered, by people who are acquainted with digital computers, to be both time-consuming and memory extensive. Depending on the size of the vectors and the matrices, and depending on the speed of memory access, this operation may require several seconds and many tens of thousands of memory locations. Consequently, the computers required to perform this operation have high-capacity memories, and they are costly.
Several examples are known in the prior art of the use of electro-optical systems for matrix-vector multiplication to circumvent the dependence upon computers for such operations. Examples of such may be found in U.S. Pat. Nos. 3,305,669 of Fan, 3,588,486 of Rosen, 3,944,820 of Stotts, and 4,009,380 of Bocker et al. Some of these systems depend upon optical masks or the equivalent (either transmissive or reflective) in modulating light energy. The Stotts patent uses polarized light in conjunction with successive phase-synchronized modulators and optical waveguides.
U.S. Pat. Nos. 3,906,220 of Delingat and 3,937,952 of Ripley et al have been found which use intermixed sets of optical fibers for various specific purposes. The former is directed to an optical correlator, whereas the latter is directed to use in a keyboard for multi-digit encoding.
The present invention employs to particular advantage in a matrix multiplying system an integral array of substantially identical, fiber optic couplers. These couplers are of the unidirectional type, referred to as launch couplers, disclosed for example in my U.S. Pat. No. 4,307,933 entitled OPTICAL FIBER LAUNCH COUPLER, of which I am named as inventor with Phillip B. Ward, Jr. The fabrication of an array of such launch couplers is disclosed in U.S. application Ser. No. 333,955 filed Dec. 23, 1981, entitled FIBER OPTIC COUPLER ARRAY AND FABRICATION METHOD of John P. Palmer and Phillip B. Ward, Jr., assigned to the assignee of this invention. The disclosure of that application is incorporated herein by reference. In brief, an array of substantially identical launch couplers is fabricated by preparing first and second support blocks with pluralities of parallel grooves and placing appropriate optical fibers in the grooves. Each launch coupler comprises a launch fiber and a throughput fiber. Epoxy resin is applied to embed the respective fibers in their blocks and then the resin and embedded fibers are lapped to develop opposed mating planar surfaces. The launch fibers are lapped entirely through the cores to expose severed end surfaces of generally elliptical shape. The throughput fibers are lapped only deep enough to expose a corresponding surface of like extent and dimensions. The two blocks are then joined at the planar surfaces, and the array of launch couplers is aligned while applying light signals to the input ports of two launch fibers at opposite ends of the array and monitoring the light output at the output ports of the corresponding throughput fibers until the output is maximized. Preferred apparatus for use in the alignment procedure is disclosed in U.S. Pat. No. 4,302,267 entitled OPTICAL FIBER MATING APPARATUS AND METHOD of Palmer and Ward. Afterward the two blocks are affixed to each other by epoxy resin or other suitable adhesive. An array of launch couplers fabricated in this fashion can be used as the basis of a matrix multiplier system.